We introduce a pattern matching algorithm and a bitmap reconstruction method used in document image compression. This pattern matching algorithm uses the cross entropy between two patterns as the criterion for a match. We use a physical model which is based on the finite resolution of the scanner to estimate the probability values used in cross entropy calculation. The matching algorithm is enhanced by the bitmap reconstruction method which infers a good high resolution image form a series of poor low resolution images. This bitmap reconstruction method is based on the naive image averaging method, but it uses a preprocessing smoothing filter and it is done in a higher resolution than the original image. Experimental results show that this pattern matching algorithm and this bitmap reconstruction method compare favorably to previous techniques.